Question 14 Marks
In the given figure, $\angle PSR =90, PQ =10 cm$, $QS =6 cm$ and $RQ =9 cm$, calculate the length of PR.
Answer
View full question & answer→PR = 17 cm
Questions
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16 questions · timed · auto-graded
Question 24 Marks
In the given figure, ABCD is a quadrilateral in which $BC =3 cm$, $AD =13 cm, DC =12 cm$ and $\angle ABD =$ $\angle BCD =90$. Calculate the length of AB .
Answer
View full question & answer→AB = 4 cm
Question 34 Marks
A ladder 15 m long reaches a window which is 9 m above the ground on one side of the street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. Find the width of the street.
Answer
View full question & answer→21 m
Question 44 Marks
A ladder 17 m long reaches the window of a building 15 m above the ground. Find the distance of the foot of the ladder from the building.
Answer
View full question & answer→8 m
[Hint. Let $A B$ be the ladder, $C B$ be the building and $B$ be the window.
Then, $A B=17 cm, B C=15 m$, find $A C$.]
[Hint. Let $A B$ be the ladder, $C B$ be the building and $B$ be the window.
Then, $A B=17 cm, B C=15 m$, find $A C$.]
Question 54 Marks
Two poles of height 9 m and 14 m stand vertically on a plane ground. If the distance between their feet is 12 m, find the distance between their tops.
Answer
View full question & answer→13 m
Question 64 Marks
In $\triangle ABC , \angle B =90$ and D is the mid-point of BC . Prove that
(i) $AC ^2= AD ^2+3 CD ^2$
(ii) $BC ^2=4\left( AD ^2- AB ^2\right)$.
(i) $AC ^2= AD ^2+3 CD ^2$
(ii) $BC ^2=4\left( AD ^2- AB ^2\right)$.
Answer
View full question & answer→self
Question 74 Marks
Find the altitude of an equilateral triangle of side $5 \sqrt{3} cm$.
Answer
View full question & answer→7.5 cm
Question 84 Marks
The sides of a right triangle containing the right angle are $(5 x) cm$ and $(3 x-1) cm$. If the area of the triangle be $60 cm^2$, calculate the length of the sides of the triangle.
Answer
View full question & answer→15 cm, 8 cm, 17 cm
Question 94 Marks
In a rhombus PQRS , side $PQ =17 cm$ and diagonal $PR =16 cm$.
Calculate the area of the rhombus.
Calculate the area of the rhombus.
Answer
View full question & answer→$240 cm^2$
[Hint. The diagonals of a rhombus bisect each other at right angles.
Area of a rhombus $=\frac{1}{2} \times$ (product of diagonals). $]$
[Hint. The diagonals of a rhombus bisect each other at right angles.
Area of a rhombus $=\frac{1}{2} \times$ (product of diagonals). $]$
Question 104 Marks
Two poles of height 9 m and 14 m stand vertically on a plane ground. If the distance between their feet is 12 m , find the distance between their tops.
Answer
View full question & answer→13 = m
Question 114 Marks
In $\triangle ABC , \angle B =90^{\circ}$ and D is the mid-point of BC . Prove that
(i) $AC ^2= AD ^2+3 CD ^2$
(ii) $BC ^2=4\left( AD ^2- AB ^2\right)$
(i) $AC ^2= AD ^2+3 CD ^2$
(ii) $BC ^2=4\left( AD ^2- AB ^2\right)$
Answer
View full question & answer→self
Question 124 Marks
Find the altitude of an equilateral triangle of side $5 \sqrt{3} cm$.
Answer
View full question & answer→7.5 cm
Question 134 Marks
The sides of a right triangle containing the right angle are $(5 x) cm$ and $(3 x-1) cm$. If the area of the triangle be $60 cm^2$, calculate the length of the sides of the triangle.
Answer
View full question & answer→$15 cm, 8 cm, 17 cm \quad$
Question 144 Marks
In the given figure, $\angle PSR =90^{\circ}, PQ =10 cm$, $QS =6 cm$ and $RQ =9 cm$, calculate the length of PR.
Answer
View full question & answer→$PR =17 cm$
Question 154 Marks
In the given figure, ABCD is a quadrilateral in which $B C=3 cm$, $AD =13 cm, DC =12 cm$ and $\angle ABD =$ $\angle BCD =90^{\circ}$. Calculate the length of AB .
Answer
View full question & answer→$AB =4 cm$
Question 164 Marks
A ladder 15 m long reaches a window which is 9 m above the ground on one side of the street. Keeping its foot at the same point, the ladder is turned to the other side of the street to reach a window 12 m high. Find the width of the street.
Answer
View full question & answer→21 m